Home > Research > Publications & Outputs > States of self-stress in symmetric frameworks a...

Electronic data

  • stresses_symmetry_revised

    Rights statement: This is the author’s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures, 234-235, 2022 DOI: 10.1016/j.ijsolstr.2021.111238

    Accepted author manuscript, 1.4 MB, PDF document

    Embargo ends: 31/08/22

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

Links

Text available via DOI:

View graph of relations

States of self-stress in symmetric frameworks and applications

Research output: Contribution to journalJournal articlepeer-review

Published

Standard

States of self-stress in symmetric frameworks and applications. / Schulze, Bernd; Miller, Cameron; Mazurek, Arek; Baker, William.

In: International Journal of Solids and Structures, Vol. 234-235, 111238, 31.01.2022.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Schulze, B, Miller, C, Mazurek, A & Baker, W 2022, 'States of self-stress in symmetric frameworks and applications', International Journal of Solids and Structures, vol. 234-235, 111238. https://doi.org/10.1016/j.ijsolstr.2021.111238

APA

Schulze, B., Miller, C., Mazurek, A., & Baker, W. (2022). States of self-stress in symmetric frameworks and applications. International Journal of Solids and Structures, 234-235, [111238]. https://doi.org/10.1016/j.ijsolstr.2021.111238

Vancouver

Schulze B, Miller C, Mazurek A, Baker W. States of self-stress in symmetric frameworks and applications. International Journal of Solids and Structures. 2022 Jan 31;234-235. 111238. https://doi.org/10.1016/j.ijsolstr.2021.111238

Author

Schulze, Bernd ; Miller, Cameron ; Mazurek, Arek ; Baker, William. / States of self-stress in symmetric frameworks and applications. In: International Journal of Solids and Structures. 2022 ; Vol. 234-235.

Bibtex

@article{6c18e736b3b74e4f819790c36f08efcb,
title = "States of self-stress in symmetric frameworks and applications",
abstract = "We use the symmetry-extended Maxwell rule established by Fowler and Guest to detect states of self-stress in symmetric planar frameworks. The dimension of the space of self-stresses that are detectable in this way may be expressed in terms of the number of joints and bars that are unshifted by various symmetry operations of the framework. Therefore, this method provides an efficient tool to construct symmetric frameworks with many {\textquoteleft}fully-symmetric{\textquoteright} states of self-stress, or with {\textquoteleft}anti-symmetric{\textquoteright} states of self-stress. Maximising the number of independent self-stresses of a planar framework, as well as understanding their symmetry properties, has important practical applications, for example in the design and construction of gridshells. We show the usefulness of our method by applying it to some practical examples.",
keywords = "Symmetry, Rigidity, Bar-joint framework, Equilibrium stress, Gridshell structure",
author = "Bernd Schulze and Cameron Miller and Arek Mazurek and William Baker",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures, 234-235, 2022 DOI: 10.1016/j.ijsolstr.2021.111238",
year = "2022",
month = jan,
day = "31",
doi = "10.1016/j.ijsolstr.2021.111238",
language = "English",
volume = "234-235",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Limited",

}

RIS

TY - JOUR

T1 - States of self-stress in symmetric frameworks and applications

AU - Schulze, Bernd

AU - Miller, Cameron

AU - Mazurek, Arek

AU - Baker, William

N1 - This is the author’s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures, 234-235, 2022 DOI: 10.1016/j.ijsolstr.2021.111238

PY - 2022/1/31

Y1 - 2022/1/31

N2 - We use the symmetry-extended Maxwell rule established by Fowler and Guest to detect states of self-stress in symmetric planar frameworks. The dimension of the space of self-stresses that are detectable in this way may be expressed in terms of the number of joints and bars that are unshifted by various symmetry operations of the framework. Therefore, this method provides an efficient tool to construct symmetric frameworks with many ‘fully-symmetric’ states of self-stress, or with ‘anti-symmetric’ states of self-stress. Maximising the number of independent self-stresses of a planar framework, as well as understanding their symmetry properties, has important practical applications, for example in the design and construction of gridshells. We show the usefulness of our method by applying it to some practical examples.

AB - We use the symmetry-extended Maxwell rule established by Fowler and Guest to detect states of self-stress in symmetric planar frameworks. The dimension of the space of self-stresses that are detectable in this way may be expressed in terms of the number of joints and bars that are unshifted by various symmetry operations of the framework. Therefore, this method provides an efficient tool to construct symmetric frameworks with many ‘fully-symmetric’ states of self-stress, or with ‘anti-symmetric’ states of self-stress. Maximising the number of independent self-stresses of a planar framework, as well as understanding their symmetry properties, has important practical applications, for example in the design and construction of gridshells. We show the usefulness of our method by applying it to some practical examples.

KW - Symmetry

KW - Rigidity

KW - Bar-joint framework

KW - Equilibrium stress

KW - Gridshell structure

U2 - 10.1016/j.ijsolstr.2021.111238

DO - 10.1016/j.ijsolstr.2021.111238

M3 - Journal article

VL - 234-235

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

M1 - 111238

ER -